Int
er
n
at
i
onal
Journ
al of Ele
ctrical
an
d
Co
mput
er
En
gin
eeri
ng
(IJ
E
C
E)
Vo
l.
9
, No
.
6
,
Decem
ber
201
9,
pp. 4
873~
4881
IS
S
N: 20
88
-
8708
,
DOI: 10
.11
591/
ijece
.
v9
i
6
.
pp4873
-
48
81
4873
Journ
al h
om
e
page
:
http:
//
ia
es
core
.c
om/
journa
ls
/i
ndex.
ph
p/IJECE
Perform
ance ana
lysis of
directi
on of
arri
val
algorit
hm
s
for
smart
a
ntenn
a
Btissam B
ou
s
t
an
i
,
Abde
nn
ac
eur Ba
ghda
d
, A
ic
h
a Sa
hel,
Ab
delm
aj
id
B
ad
ri
La
bora
tor
y
El
e
ctronics,
Ene
rg
y
,
Autom
at
ic
and
I
nform
at
ion
Proc
essing,
E
lectr
i
cal
Eng
ine
er
ing
D
epa
rtment
,
Fac
ulty
of
Sci
en
ce
and Technolo
g
y
Moham
m
edi
a,
Hass
an
II
Univ
ersity
C
asa
bla
n
c
a
,
Moro
cc
o
Art
ic
le
In
f
o
ABSTR
A
CT
Art
ic
le
history:
Re
cei
ved
J
un
8
, 201
8
Re
vised
Jun
2
5
, 201
9
Accepte
d
J
ul
6
, 201
9
Thi
s
pape
r
pr
ese
nt
s
the
p
erf
or
m
anc
e
anal
y
s
is
of
the
dir
ec
t
io
n
of
arr
ival
esti
m
at
ion
al
gor
i
thms
such
as
Est
imati
on
of
Signal
Para
m
et
ers
via
Rota
ti
on
a
l
Inva
ria
n
ce
T
ec
h
nique
(ESPR
IT)
,
Multi
ple
Sign
al
Cla
ss
ifi
c
ation
(MU
SIC),
W
ei
ghte
d
Subs
pac
e
Fitt
ing
(W
SF
),
The
Minim
um
Vari
anc
e
Distorti
onl
ess
Response
(MV
D
R
or
ca
pon)
and
b
ea
m
spac
e
.
Thes
e
al
gori
thms
are
necess
a
r
y
to
over
come
th
e
proble
m
of
d
et
e
ct
ing
the
arr
i
val
ang
le
s
of
t
he
recei
v
ed
signal
s
in
wire
les
s
com
m
unic
at
io
n.
The
ref
or
e,
th
e
se
al
gorit
hm
s
are
eva
lu
at
ed
and
compare
d
a
cc
ording
to
sev
era
l
constra
in
ts
req
uire
d
in
sm
art
an
t
enna
s
y
stem
par
amet
ers,
as
the
numbe
r
of
arr
a
y
e
lem
ent
s,
num
ber
of
sam
ple
s
(snapshots),
and
num
ber
of
the
rec
e
ive
d
sign
al
s.
The
m
ai
n
purp
ose
of
thi
s
stud
y
is
to
obt
ain
the
b
est
esti
m
a
ti
on
of
th
e
dir
ect
ion
of
arr
iva
l
,
w
hic
h
c
an
be
per
fectl
y
imple
m
ent
ed
in
a
sm
art
antenna
s
y
st
e
m
.
In
thi
s
con
te
x
t,
th
e
ROO
T
-
W
ei
ghte
d
Subs
p
ac
e
Fitt
ing
al
gor
it
hm
provide
s
th
e
m
ost
a
cc
ura
te
det
e
ct
ion
of
arr
ival
angl
es
in ea
ch
of the
prop
osed
sce
na
rios.
Ke
yw
or
d
s
:
DOA
al
gorith
m
ESPRIT
MUSIC
MVDR
Roo
t
-
M
us
ic
Roo
t
-
WSF
Sm
art antenn
a
s
yst
e
m
WSF
Copyright
©
201
9
Instit
ut
e
o
f Ad
vanc
ed
Engi
n
ee
r
ing
and
S
cienc
e
.
Al
l
rights re
serv
ed
.
Corres
pond
in
g
Aut
h
or
:
Bt
issam
B
ou
sta
ni,
Lab
or
at
ory
Ele
ct
ronics, E
nerg
y, A
uto
m
at
ic
a
nd Info
rm
ation Processi
ng,
Dep
a
rtm
ent
of
Ele
ct
rical
En
gi
neer
i
ng,
Facu
lt
y o
f
Scie
nce a
nd Tec
hnology M
oham
m
edia,
Hassa
n
I
I U
nive
rsity
Casablan
ca
B.P.
14
6
M
oh
am
m
edia 2
0650 M
orocc
o
.
Em
a
il
: bti
ssa
m
.bou
sta
ni@
gma
il
.co
m
1.
INTROD
U
CTION
Currentl
y,
m
a
ny
resea
rc
her
s
are
inte
rested
in
new
te
c
hn
ologies
s
uch
a
s
the
In
te
r
net
of
Thi
ng
s
a
nd
the
5th
ge
nerat
ion
,
to
t
rack
the
e
xcessi
ve
gro
wth
of
w
irel
ess
te
ch
no
l
og
ie
s
.
T
his
e
xponentia
l
pro
gr
es
s
gen
e
rates
incr
eased
dem
and
fo
r
capa
ci
ty
[1
]
,
a
need
f
or
m
or
e
rad
io
f
r
equ
e
ncies
[
2],
excessive
ap
pe
al
fo
r
sign
al
processi
ng
an
d
sp
ace
c
on
st
raints
[3
]
,
w
hic
h
ca
nnot
be
sat
isfie
d
us
i
ng
Co
nventio
na
l
anten
nas,
de
sp
it
e
the
i
m
pr
ovem
e
nts
m
ade
in
th
e
cov
e
rag
e
a
re
a
[3
]
.
More
ove
r,
the
us
e
of
pa
ssive
anten
nas
le
ads
to
a
sign
i
ficant
energy
wastag
e,
a
m
ajor
int
erf
e
ren
ce
fact
or
in
c
o
-
cha
nnel
,
wh
ic
h
i
nc
it
es
researc
hers
to
seek
al
te
r
native
strat
egies to
ov
erco
m
e these e
ncou
ntere
d pro
blem
s.
Sm
art
antenn
a
te
chn
ol
og
y
is
con
si
der
ed
as
the
best
so
lut
ion
co
nfr
on
ti
ng
thes
e
pro
ble
m
s.
It
can
achieve
high
ly
eff
ic
ie
nt
netw
ork,
m
axi
m
iz
i
ng
t
he
ca
pacit
y
and
im
pr
ovin
g
qual
it
y
and
c
ov
e
ra
ge
[
4
,
5]
.
It
al
so
ref
e
rr
e
d
to
ada
ptive
a
rr
ay
a
ntenn
a
s
[
6]
,
te
nd
s
towa
r
d
creati
ng
an
ada
ptive
beam
fo
rm
ing
us
in
g
a
na
rrow
beam
in
directi
on
of
the
de
sired
s
ign
al
wh
il
e
ca
nceli
ng
the
i
nt
erf
ere
nce
si
gnal
s.
These
ant
enn
a
s
are
us
e
d
f
or
m
illim
e
te
r
wa
ves
(m
m
-
wav
e
),
Ra
di
o
F
requen
cy
Id
e
ntifi
cat
ion
(R
FID)
,
Mult
iple
Inp
uts
Mult
iple
Ou
t
pu
ts
(MIMO
),
a
nd s
o on.
Sm
art
antenn
a
syst
e
m
con
ta
ins
tw
o
m
ajor
f
un
ct
io
ns,
knowin
g
as
t
he
di
recti
on
of
a
rr
i
val
est
im
a
ti
on
(DOA)
a
nd
t
he
beam
fo
rm
ing
giv
e
n
by
a
da
ptive
al
gorithm
s.
The
cl
as
sic
al
m
od
el
of
the
s
m
art
antenn
a
s
yst
e
m
is co
ns
ide
r
ed
a
s sho
wing in
Fi
gure
1
[7]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8708
In
t J
Elec
&
C
om
p
En
g,
V
ol.
9
, N
o.
6
,
Dece
m
ber
2
01
9
:
4873
-
4881
4874
Figure
1
.
Bl
oc
k diag
ram
of
s
m
art anten
na
s
yst
e
m
[
3
]
The
directi
on
of
ar
rival
(
DOA)
is
on
e
of
the
m
os
t
chall
e
ng
i
ng
prob
le
m
s
fo
r
locat
in
g
and
trac
king
m
ul
ti
ple
m
ov
ing
s
ources
in
diff
e
ren
t
area
s,
su
c
h
as
radar
[8
]
,
s
onor
[9
]
,
an
d
m
ob
il
e
co
m
m
un
ic
at
ion
s.
The
locat
io
n
of
source
s
with
distrib
uted
se
nsor
a
rr
ay
s
ca
n
be
achie
ved
by
est
i
m
a
ti
ng
the
directi
on
of
a
r
rival
of sig
nals fr
om
te
rm
inal
so
ur
c
es
[
10
,
11
]
.
Var
i
ou
s
te
c
hn
i
qu
e
s
are
use
d
to
est
i
m
at
e
the
directi
on
of
arr
ival,
am
ong
wh
ic
h
are
high
-
res
olu
ti
on
m
et
ho
ds
s
uc
h
as
Estim
at
io
n
of
Sig
nal
P
aram
et
ers
via
Rotat
ion
al
I
nv
ariance
Tec
hn
iqu
e
(ESP
R
IT
)
[
12
]
,
Mult
iple
Signal
Cl
assifi
cati
on
(M
USIC)
[
13
]
,
W
ei
ghte
d
S
ubs
pace
F
it
ti
ng
(
W
S
F)
[
14
]
,
The
Mi
nim
u
m
Var
ia
nce
Distortio
nless
Re
s
pons
e
(M
VD
R
or
ca
pon)
[
15
]
and
beam
sp
a
ce,
these
te
ch
ni
qu
es
ha
ve
at
tract
ed
the
m
os
t
interest
and
has
be
e
n
the
s
ubj
ect
of
m
any
stud
ie
s
[
10
-
15
]
,
howe
ver,
none
of
th
ese
stud
ie
s
rea
ched
the b
e
st
pe
rform
ance in
sm
art anten
nas
.
In
this
pap
e
r,
we
fo
c
us
e
d
on
one
of
the
m
ai
n
f
unct
ions,
wh
ic
h
is
t
he
di
recti
on
of
ar
ri
val,
a
nd
we
stud
ie
d
al
l
the
possibil
it
ie
s
of
bette
r
perf
orm
ance.
To
do
so
,
we
first
inv
e
sti
gate
d
th
e
al
gorithm
s
t
hat
w
e
work
ed
with
,
wh
ic
h
a
re
bea
m
scan,
MUS
I
C,
r
oo
t
-
MUS
I
C,
ESPR
IT,
ca
pon
or
M
VD
R
,
r
oot
-
WSF
.
T
hen
we
evaluate
d
our
s
yst
e
m
accor
di
ng to
the
f
ollow
i
ng crite
rio
n:
a.
The n
um
ber
of
arr
ay
elem
ents
b.
The n
um
ber
of
sam
ple
s
c.
The n
um
ber
of
sig
nal
s
Finall
y,
we
m
at
ched
the
syst
e
m
with
the
corres
p
on
ding
pa
ram
et
ers
of
sm
art
antenn
a;
in
this
case
,
we wil
l wor
k wit
h W
i
-
Fi
para
m
et
ers
as a te
sti
ng
e
xam
ple.
2.
RESEA
R
CH MET
HO
D
2.1.
DOA es
tima
tion
The
m
ai
n
r
ole
of
the
D
OA
is
to
est
im
a
te
the
directi
on
of
th
e
desire
d
sig
na
l
by
c
ollec
ti
ng
data
from
the
inc
om
ing
si
gn
al
s
r
ecei
ve
d
by
the
a
nten
na
arr
ay
[
16
]
.
A
dap
ti
ve
al
gorit
hm
s
are
the
ba
ckbo
ne
of
the
sm
ar
t
anten
na
syst
em
.
They
consi
st
of
creati
ng
a
dju
sta
ble
beam
s
that
m
eet
the
dem
and
s
of
the
syst
e
m
.
These
al
gorith
m
s
us
e
a
set
of
com
plex
wei
ghts
to
a
djust
th
e
am
pli
tud
e
or
the
phase o
f
ea
ch
el
em
ental
a
nten
na
of
the
pro
pose
d
netw
ork.
T
he
trai
ne
d
syst
e
m
can
on
ly
operate
by
knowin
g
the
a
ng
l
es
of
a
rr
i
val,
wh
e
re
the esti
m
a
ti
on
of the
directi
on
of arrival
al
gorithm
s is then
re
qu
i
red
[
17
]
.
2.2.
Conv
e
nt
i
on
al
DOA
The
c
onve
ntio
nal
D
O
A
bea
m
fo
r
m
ing
m
eth
od
is
al
s
o
know
n
as
t
he
Ba
rtle
tt
m
e
thod,
c
onsist
of
a
powe
r
stu
dy,
in
w
hich,
ove
r
a
scan
acr
os
s
the
an
gu
la
r
re
gion
of
inte
res
t,
look
f
or
the
la
rg
est
out
pu
t
powe
r
from
the
diff
e
r
ent d
i
recti
on to
estim
at
e the desi
red
one
[18]
.
It
is
al
so
a
p
pro
pr
ia
te
t
o
proceed
to
the
sp
at
ia
l
sp
ect
r
um
m
e
tho
d
i
n
w
hich
the
e
stim
ation
of
the
directi
on
is
m
ade
on
ly
by
cor
re
spo
ndin
g
the
pea
k
value
of
the
ou
tp
ut
pow
e
r
with
the
an
gle
ϴ
.
The
e
xpressi
on of the
Bartl
et
t m
et
ho
d
ca
n be
giv
e
n by:
(
)
=
(
)
(
)
(
)
(
)
(1)
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
Elec
&
C
om
p
En
g
IS
S
N: 20
88
-
8708
Perf
orma
nce
analysis
of
direc
ti
on
of arri
val
algorit
hms fo
r
smart a
nten
na
(
Bti
ssa
m
B
oustan
i)
4875
w
it
h:
=
(
)
(
)
(
2)
In
this
e
xpress
ion
,
a(
θ)
an
d
RXX
re
pr
ese
nt
res
pecti
vely
the
ar
ray
respon
s
e
vecto
r
a
nd
th
e
a
uto
c
ov
a
rian
c
e
m
at
rix
of the
re
cei
ved
sig
nal.
2.3.
MVD
R
(
C
apo
n a
l
go
ri
th
m
)
Mi
ni
m
u
m
Var
ia
nce
Disto
rtio
nless
Re
spon
se
or
Ca
pon
be
a
m
fo
r
m
er
is
a
s
olu
ti
on
f
or
the co
nve
ntio
nal
beam
fo
rm
er
(the
Ba
rtle
tt
m
et
hod)
pro
ble
m
caused
w
he
n
the
s
ource
s
to
be
l
ocated
a
re
cl
ose
r
tha
n
the
beam
width.
Wh
e
n
the
B
artl
et
t
m
et
ho
d
can’
t
se
pa
rate
them
,
the
MVDR
te
c
hn
i
que
interfe
re
s
to
so
lv
e
the
pro
blem
[
19
].
The
only
ad
j
us
tm
ent
m
ade
in
the
c
onve
nt
ion
al
be
a
m
fo
rm
er
is
the
ad
diti
on
al
m
a
trix
inv
e
rsion R
xx
, i
n wh
ic
h
the
Ca
pon
s
patia
l spe
ct
ru
m
is g
ive
n by:
(
)
=
1
(
)
−
1
(
)
(3)
2.4.
MUSIC
a
l
gori
th
m
The
M
ulti
ple
S
ign
al
Cl
assifi
c
at
ion
(M
USIC)
al
gorithm
is
widely
us
e
d
i
n
ada
ptive
a
nten
nas
because
of
t
he
go
od
r
esult
est
i
m
at
in
g
the
directi
on
of
ar
rival
s
pecifi
cal
ly
when
the
si
gn
al
s
a
re
unc
orrelat
ed
an
d
the
num
ber
of
so
urce
s
is
kn
own
[
20
,
21]
.
T
his
m
et
ho
d
reli
es
on
t
he
Ei
ge
ns
tr
uctu
re
of
i
nput
c
ovaria
nce
m
at
rix
[21].
T
her
e
f
ore,
we
ch
os
e
to
wor
k
with
the
sig
nal
value
deco
m
po
sit
ion
(
S
VD
)
te
chn
i
qu
e
,
of
w
hic
h
the cova
riance
m
at
rix
is re
pr
e
s
ented
as
fo
ll
ows:
=
=
+
2
(4)
And
2
rep
re
se
nt
res
pecti
vely
the
sign
al
par
t
an
d
the
no
ise
par
t,
w
her
e
Us
is
the
sig
nal
s
ubspa
ce
c
orres
pondin
g
t
o
V
s
an
d
U
n
is
the
no
ise
sub
sp
ace
with
th
e
noise
var
ia
nce
2
.
The
e
xpressi
on of
norm
alized
MUSIC
sp
ect
r
um
is g
iven
b
y
:
(
)
=
(
)
(
)
(
)
(
)
(5)
In li
te
ratur
e,
th
is ex
pr
essi
on c
ou
l
d be
wr
it
te
n as
:
(
)
=
1
(
)
(
)
(6)
2.5.
Root
-
MUSIC
Roo
t
-
M
USIC
is
consi
der
e
d
a
s
on
e
of
m
any
conversi
on
of
MUSIC
al
gor
it
h
m
,
it
is
base
d
on
set
ti
ng
up
the
r
oots
of
a
po
ly
no
m
ia
l,
this
te
chn
iqu
e
aim
s
to
decr
e
ase
the
com
pu
ta
ti
on
al
com
plexity
and
i
m
pr
ove
it
s
perform
ance. Neve
rt
heless
,
i
t i
s appli
cable
on
ly
for
a li
ne
a
r
ar
ray
s
paced
un
i
form
l
y [
17
]
.
2.6.
ESPRIT
a
lg
or
ithm
Estim
at
ion
of
Sign
al
Param
et
ers
via
Rotat
ion
al
Invar
ia
nc
e
Techn
i
qu
e
(ESP
R
IT),
is
a
su
bspace
te
chn
iq
ue,
use
d
to
e
stim
at
e
the
an
gle
of
a
rr
ival
(AO
A)
by
determ
inin
g
the
r
otati
onal
op
e
rato
r
Ф
[
2
1
].
ESPRIT
al
gori
thm
sh
ow
s
sa
m
e
per
f
or
m
ance
as
MUSIC
al
go
rithm
with
sli
ght
ad
justm
ent
.
T
he
aim
s
of
ESPRIT
strat
e
gy
is
to
m
isuse
the
ro
ta
ti
on
a
l
inv
ariance
in
the
flag
subspa
ce
,
wh
ic
h
is
m
ade
by
two
cl
us
te
r
s
with
a
transla
ti
on
al
inv
a
rian
ce
structu
re
[
2
2
].
E
SPRIT
al
gorithm
hav
e
sever
al
a
dvantages
pr
ese
nt
ed
i
n
the
si
m
plici
t
y
of
Im
plem
enta
ti
on
,
pr
oducin
g
directi
on
of
arr
ival
directl
y
avo
idi
ng
the
s
earch
proce
dur
e,
do
e
s
no
t
need
m
uch
com
pu
ta
ti
on
or
st
or
a
ge
re
quirem
ent.
Consi
der
in
g
a
li
ne
a
r
ar
ray
with
t
wo
double
ts
a
nd
fou
r
el
e
m
ent
s
, th
e t
wo suba
rr
ay
s a
re r
ecei
ve
d by
[2
1
]
.
1
(
)
=
∗
(
)
+
1
(
)
(7)
2
(
)
=
∗
∧
∗
(
)
+
2
(
)
(8)
w
he
re
∧
=
{
1
,
2
,
…
,
}
(9)
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:
4873
-
4881
4876
=
−
2
(
)
(10)
λ
=
(11)
Wh
e
re
D<M
(
nu
m
ber
of
sig
nal
hitt
in
g
the
subar
rays)
.
T
he
tw
o
m
a
trix
V
1
a
nd
V
2
are
cre
at
ing
by
t
w
o
su
ba
r
rays
,
i
n
wh
ic
h
t
he
ei
ge
nv
ect
or
s
are
relat
ed
by
a
uniq
ue
nons
i
ngular
t
ran
s
f
or
m
at
ion
m
at
rix
ф
with
a
un
i
qu
e
no
ns
in
gula
r
tra
nsfo
rm
a
ti
on
m
at
rix
T.
2
=
ф
1
(12)
1
=
(13)
2
=
∧
(14)
Tha
n
∧
=
T
ф
−
1
(15)
The
ei
ge
nval
ue
s
of
ф
(λi)
m
us
t
be
e
qual
to
the
diag
onal
el
e
m
ents
of
Λ.
On
ce
t
he
ei
ge
nv
al
ues
ar
e
cal
culat
ed
the
est
i
m
ation
of the a
ng
le
of ar
ri
val can
b
e
m
ade b
y:
=
−
1
(
a
rg
(
λ
)
)
(16)
2.7.
WSF
a
lg
orith
m
Weig
hted
S
ubs
pace
F
it
ti
ng
(
WSF)
al
gorith
m
is
an
asym
pt
otica
ll
y
pr
ofi
ci
ent
pa
ram
et
ric
m
et
ho
d
us
e
d
for
est
i
m
at
ing
the
heigh
ts
of
di
ff
e
ren
t
s
cat
te
rer
s
in
th
e
sa
m
e
azim
u
th
-
ra
nge
res
olu
ti
on
cel
l
[
2
3
,
2
4
].
Like
the
MUS
I
C
and
ESPR
IT
al
go
rithm
s,
the
WSF
al
gorit
hm
rep
resen
ts
a
un
ifie
d
ap
pro
ach
that
al
so
sta
nd
in
needs
of
the
knowle
dge
of
th
e
nu
m
ber
of
directi
on
al
s
ourc
es,
an
d
the
us
e
of
th
e
dec
om
po
sit
ion
te
c
hn
i
que
f
or
ei
genvalues
.
the
str
ongest
e
igen
vecto
rs
in
a
diagonal
m
at
rix
(
̂
)
an
d
th
e
correspo
nd
i
ng
ei
ge
nv
ect
or
s
in
the
sig
nal
s
ubs
pace
m
at
rix
(
̂
)
[
2
5
]
are
us
e
d
to
acc
om
plish
this
a
ppro
ac
h.
The
e
xpressi
on
of
WSF
al
gori
thm
can
be writt
en a
s:
̂
=
(
(
П
(
)
̂
̂
)
)
(17)
П
(
)
re
pr
ese
nte
T
he
pro
j
ect
ion
m
at
rix
onto
the
c
olu
m
n
sp
ace
of
a(θ),
an
d
W
is
a
weig
htin
g
m
at
rix
to r
e
duce the
im
pact o
f
the
subspa
ce s
wap
[
2
6
].
2.8.
Root
-
W
SF
a
lg
orithm
Roo
t
-
WSF
is
t
he
rootin
g
versi
on
of
Weig
ht
ed
S
ubs
pace
F
it
ti
ng
,
al
so
re
f
err
e
d
as
MO
D
E
te
c
hniq
ue.
The
ai
m
s o
f
t
his m
et
ho
d
is t
o
m
ini
m
iz
e the c
os
t f
unct
ion
wi
th
[
27
]
.
(
)
=
(
(
)
⊥
̂
̂
)
(18)
Wh
e
re:
(
)
⊥
=
−
(
)
(
(
)
(
)
)
−
1
(
)
(19)
=
(
̂
−
̂
2
)
̂
−
1
(20)
̂
2
=
1
−
(
̂
)
(21)
corres
pond
to
the
asy
m
pto
ti
c
-
opti
m
u
m
wei
gh
t
m
at
rix
,
2
is
the
no
ise
va
rian
ce
an
d
(
)
⊥
ind
ic
at
e
the
or
t
hogonal
pro
j
ect
ion m
at
rix
of the a
rr
ay
ste
erin
g
m
at
rix
[
24
,
2
8
].
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p
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88
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Perf
orma
nce
analysis
of
direc
ti
on
of arri
val
algorit
hms fo
r
smart a
nten
na
(
Bti
ssa
m
B
oustan
i)
4877
3.
RESU
LT
S
A
ND AN
ALYSIS
In
order
to
e
va
luate
the
perform
ance
s
of
the
diff
e
ren
t
di
rec
ti
on
of
arr
i
val
al
gorithm
s
,
three
scenari
os
hav
e
bee
n
m
a
de,
ba
sed
on
t
he
cha
ng
i
ng
pa
ram
et
ers
of
the
num
ber
of
sig
nals,
th
e
nu
m
ber
of
sam
pl
es
and
the
num
ber
of
ar
ray
el
em
ents.
F
or
this
reas
on
we
c
onside
r
a
unif
or
m
li
near
ar
ray
(U
L
A
)
of
M
t
he
nu
m
ber
of
el
e
m
entary
antenn
a
s
with
the
inter
-
el
em
ent
sp
aci
ng
of
λ/2,
wh
ere
λ
is
th
e
wav
el
en
gth
of
inci
den
t
ra
di
at
ion
,
K
re
pr
es
ents
th
e
nu
m
ber
of
sa
m
ples
or
sn
a
psho
ts
a
nd
the
a
ngle
s
of
ar
rival
is
giv
e
n
by
A
OA
.
All
the
s
ources
are
co
ns
ide
red
un
c
orrelat
ed
with
the
sam
e
fr
e
qu
e
ncy
of
1
GH
z
an
d
wit
h
identic
al
pow
er.
The
se
sim
u
la
ti
on
s
pr
ese
nted
in
t
hi
s secti
on
a
re
pe
rfor
m
ed
with
MATLAB
and
SI
M
ULIN
K
R
2015a.
3.1.
Result
of
a
s
p
at
i
al s
pec
trum
In
this
pa
rt,
we
will
evaluate
t
he
D
OA
al
gori
thm
s
based
on
the
sp
at
ia
l
sp
ect
ru
m
stud
y.
Fo
r
that,
w
e
pro
po
se
d
a
sy
stem
.
The
para
m
et
ers
of
th
e
pro
posed
sy
stem
can
see
in
Ta
ble
1.
T
he
resu
lt
s
of
these
si
m
ulati
on
s ar
e
presente
d
as
F
igure
2
, Fi
gure
3
a
nd Fi
gure
4.
Table
1
.
Param
et
ers
of t
he pr
opose
d sy
ste
m
Para
m
eters
Valu
e
An
ten
n
a
ULA
Nu
m
b
e
r
o
f
th
e ele
m
e
n
ts (
M)
10
Sp
acin
g
between
e
le
m
en
ts (
D)
λ
/2
Receiv
ed
sig
n
als (S)
3
An
g
les o
f
ar
rival (
AOA)
ϴ
1
=
-
3
0
°;
ϴ
2
= 0°;
ϴ
3
=2
0
°
Nu
m
b
er
of
sa
m
p
l
es (K)
1024
Figure
2
.
C
onve
ntion
al
beam
fo
rm
ing
Figure
3. MV
DR a
lg
or
it
hm
Figure
4. MUS
IC a
lg
or
it
hm
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In
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om
p
En
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V
ol.
9
, N
o.
6
,
Dece
m
ber
2
01
9
:
4873
-
4881
4878
The
res
ults
obta
ined
s
how
three
dif
fer
e
nt
al
gorithm
s
.
Fig
ur
e
2
c
orres
ponds
t
o
the
cl
assic
Be
a
m
fo
rm
ing
giv
in
g
unreli
able
res
ults,
w
her
e
the
pro
pose
d
arr
i
val
ang
le
s
a
re
not
detect
able.
Fi
gure
3
ind
ic
at
es
that
the
MV
DR
al
go
rithm
pr
ovide
s
an
acce
ptabl
e
resu
lt
com
par
ed
to
the
c
onven
ti
onal
al
gor
it
h
m
.
Howe
ver,
the
a
ng
le
of
ar
rival
of
ϴ
2
=
0
°
is
not
co
nceiva
ble.
Fig
ur
e
4
repre
sents
the
M
USIC
al
gorithm
wh
ic
h
giv
es
the
s
harpest
an
d
cl
earest
resu
lt
a
m
on
g
the
th
ree
AOAs.
T
her
e
f
or
e
,
we
can
c
ertai
n
ly
con
cl
ud
e
that
the MUS
IC al
gorithm
sti
pu
la
te
s
the
best
resul
t.
3.2.
DOA c
ompari
so
n
In
t
his
sect
io
n,
we
will
analy
ze
the
perform
a
nces
of
the
different
DOA
al
gorithm
s,
in
ord
er
to
l
ocate
the
arr
i
val
an
gl
es
and
e
xtract
the
best
m
et
ho
d.
T
he
pro
po
sed
syst
em
re
m
ai
ns
the
sam
e
as
show
n
in
Table
1
.
The
T
able
2
presents
this
st
udy
.
Ta
ble
2
is
consi
ste
nt
with
the
st
ud
y
f
ound
in
the
sp
at
i
al
sp
ect
r
um
m
et
hod,
in
w
hich
the
MUSIC
al
gorithm
pr
oves
it
s
eff
ect
ive
ness.
we
ca
n
al
s
o
se
e
that
oth
er
al
gorithm
s
li
ke
ROOT
-
MUSIC a
nd R
O
OT
-
WSF ha
ve
d
ist
in
gu
is
hed them
sel
ves
by g
ivi
ng go
od r
e
su
lt
s.
Table
2
.
C
om
par
at
ive stu
dy
of
diff
e
ren
t
D
O
A
al
go
rithm
s
Ty
p
e of
DO
A
AOA
-
30°
0°
20°
MVDR
-
31°
0°
20°
Bea
m
scan
-
31°
1°
21°
Bea
m
sp
ace
ESPRI
T
-
3
8
.92
°
-
0
.00
0
9
°
2
2
.95
°
ESPRI
T
-
4
2
.29
°
0°
1
8
.66
°
MUSI
C
-
30°
0°
20°
ROOT
-
MUS
IC
-
3
0
.53
°
-
0
.00
0
9
°
2
0
.57
°
ROOT
-
W
SF
-
30°
-
0
.00
0
5
°
20°
3.2.1.
Fir
st
scen
ario
:
V
ar
yin
g
t
he
number
of ele
ments
Af
te
r
analy
zi
ng
eac
h
D
O
A
e
stim
ation
al
go
rithm
,
we
will
evaluate
th
ei
r
perform
ance
accor
ding
to
certai
n
crit
eria.
F
irst
by
c
ha
ng
i
ng
the
nu
m
ber
of
el
em
ent
ery
arr
ay
M
from
6
to
8
then
10.
Ta
ble
3
giv
es
the r
es
ults c
orr
esp
onding t
o
t
wo num
ber
s
of elem
entary an
te
nn
as
of
6
a
nd 8
.
Wh
il
e the
num
ber
10 is
gi
ven b
y
Table
2
wh
e
re
the
D
OA
c
omparis
on
st
ud
y
was
est
ablish
e
d.
We
can
no
ti
ce
th
at
even
by
changin
g
the
nu
m
ber
of
ante
nn
as
,
t
he
best
res
ults
are
on
ly
pro
vid
ed
by
R
O
OT
-
MUS
IC
a
nd
RO
OT
-
WSF
.
As
a
res
ult,
th
e
highe
r
the num
ber
of
anten
nas, t
he m
or
e accur
at
e
the r
es
ults
will
b
e.
Table
3
.
T
he
varia
ti
on
of the
nu
m
ber
of ante
nn
a
elem
ents f
or
dif
fer
e
nt
D
OA alg
or
it
hm
s
Ty
p
e of
DO
A
AOA fo
r
N=6
AOA fo
r
N=8
-
30°
0°
20°
-
30°
0°
20°
MVDR
-
30°
0°
18°
-
27°
0°
20°
Bea
m
scan
-
30°
-
3°
20°
-
28°
-
2°
19°
Bea
m
sp
ace
ESPRI
T
-
3
2
.03
°
-
0
.00
0
7
°
2
0
.04
°
-
3
7
.36
°
-
0
.00
0
4
°
2
7
.16
°
ESPRI
T
-
3
3
.39
°
-
0
.00
0
8
°
2
2
.35
°
-
29.
47°
-
0
.00
0
3
°
2
5
.08
°
MUSI
C
-
2
6
.4°
-
0
.00
4
°
1
1
.2°
-
30°
-
1
.2°
20°
ROOT
-
MUS
IC
-
2
9
.99
°
-
0
.00
1
°
2
0
.1°
-
2
5
.4°
-
0
.00
1
5
°
2
1
.56
°
ROOT
-
W
SF
-
30°
-
0
.00
0
8
°
20°
-
30°
-
0
.00
1
°
20°
3.2.2.
2n
d
scen
ario
: Va
r
yin
g the
n
umber
of s
am
ples
The
T
able
4
re
pr
ese
nt
s
the
va
ryi
ng
num
ber
o
f
sam
ples
fr
om
10
0,
50
0,
an
d
1024,
ap
plie
d
in
differe
nt
DOA
al
go
rith
m
s.
The
ta
ble
corres
pondin
g
to
K
=
1024
i
s
the
one
with
the
com
par
iso
n
stu
dy
as
s
ho
wn
i
n
Table
2
.
Like
t
he
pr
e
vious
ta
ble,
t
he
r
esults
sho
w
that
t
he
two
al
gorithm
s
RO
OT
-
M
USIC
an
d
RO
OT
-
WSF
pro
vid
e
the
be
st
resu
lt
s.
The
ROOT
-
WSF
al
gorithm
giv
es
the
m
os
t
accurate
a
ng
le
s
of
arr
i
val
f
or
t
he
thre
e
pro
po
se
d
s
am
ples. I
t i
s als
o
tr
ue
that t
he
la
r
ge
r
the
num
ber
of sam
ples, th
e
m
or
e p
recise
it
b
ecom
es.
3.2.3.
3rd
s
cen
ario:
Va
r
yin
g the
n
umber
of sig
n
als
We
w
il
l
now
s
tud
y
the
im
pact
of
the
num
ber
of
sig
nals
on
the
D
OA
e
sti
m
at
e
.
The
ch
ose
n
nu
m
ber
s
are
2
an
d
3.
From
T
able
5
,
we
can
no
ti
ce
th
at
two
sign
al
s
on
ly
nee
d
two
ang
le
s
of
ar
riv
al
to
fu
nctio
n
,
wh
ic
h
is
obvious,
w
ha
t
is
i
m
po
rtant
to
note
is
that
fo
r
eac
h
of
t
he
D
O
A
al
gor
it
h
m
s,
we
obta
in
the
sam
e
resu
lt
,
corres
pondin
g
to
the
an
gles
of
ar
rival
that
we
see
k.
H
ow
ever,
wh
e
n
t
he
sy
stem
switc
hes
t
o
th
ree
si
gn
al
s
,
the only
alg
or
it
hm
s that enab
l
e the c
orres
pondin
g detec
ti
on
are RO
OT
-
MU
SI
C a
nd RO
O
T
-
W
SF.
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
Elec
&
C
om
p
En
g
IS
S
N: 20
88
-
8708
Perf
orma
nce
analysis
of
direc
ti
on
of arri
val
algorit
hms fo
r
smart a
nten
na
(
Bti
ssa
m
B
oustan
i)
4879
Table
4
.
T
he
va
riat
ion
of the
nu
m
ber
of sam
ples fo
r diffe
re
nt DO
A
al
go
rithm
s
Ty
p
e of
DO
A
AOA fo
r
K=1
0
0
AOA fo
r
K=5
0
0
-
30°
0°
20°
-
30°
0°
20°
MVDR
-
31°
0°
20°
-
30°
0°
20°
Bea
m
scan
-
31°
1°
20°
-
31°
1°
20°
Bea
m
sp
ace
ESPRI
T
-
30°
-
8°
1
5
.72
°
-
3
4
.97
°
-
0
.00
4
°
1
8
.27
°
ESPR
IT
-
2
9
.29
°
-
0
.00
0
1
°
1
3
.86
°
-
35°
-
0
.00
4
°
2
0
.51
°
MUSI
C
-
30°
2
.7°
20°
-
30°
0
.6°
1
9
.6°
ROOT
-
MUS
IC
-
3
1
.01
°
-
0032°
2
0
.29
°
-
3
0
.32
°
-
0
.00
0
7
°
1
9
.71
°
ROOT
-
W
SF
-
30°
-
0
.00
2
°
20°
-
30°
-
0
.00
0
2
°
20°
Table
5
.
T
he
varia
ti
on
of the
nu
m
ber
of sig
na
ls for
dif
fer
e
nt
D
O
A
al
gorith
m
s
Ty
p
e of
DO
A
AOA fo
r
S=2
AOA fo
r
S=3
-
30°
20°
-
30°
0°
20°
MVDR
-
30°
20°
-
31°
0°
20°
Bea
m
scan
-
30°
20°
-
31°
1°
21°
Bea
m
sp
ace
ESPRI
T
-
30°
20°
-
3
8
.92
°
-
0
.00
0
9
°
2
2
.95
°
ESPRI
T
-
30°
20°
-
4
2
.29
°
0°
1
8
.66
°
MUSI
C
-
30°
20°
-
30°
0°
20°
ROOT
-
MUS
IC
-
3
0°
20°
-
3
0
.53
°
-
0
.00
0
9
°
2
0
.57
°
ROOT
-
W
SF
-
30°
20°
-
30°
-
0
.00
0
5
°
20°
3.3.
Co
m
pa
r
ais
on
w
ith other
studi
es
Com
par
ing
our
stud
y
with
the
relat
ed
work
s
pr
e
viously
publishe
d,
w
e
can
noti
ce
that
eac
h
of
the
pro
posed
m
anu
scri
pts
[
29
-
3
1
]
prese
nts
an
inc
om
plete
stud
y
of
t
he
di
recti
on
of
ar
rival
est
im
at
ion
al
gorithm
s.
Th
eref
or
e
,
we
ha
ve
te
nde
d
in
this
arti
cl
e
to
c
om
plete
these
w
orks
by
br
i
ng
i
ng
to
ge
ther
al
l
the possi
bili
ti
e
s off
e
red by t
he
stat
e o
f
the
ar
t i
n
or
der
t
o
a
pply
them
to
ne
w wirel
ess tec
hnologies.
3.4.
Wi
-
Fi p
ara
me
ter
Fo
r
this
st
ud
y,
we
c
onsider
the
sam
e
pr
op
ose
d
syst
em
giv
en
in
Ta
ble
2.
T
w
o
W
i
-
Fi
fr
e
quencies
bands
a
re used
:
2.
4 G
Hz
a
nd
5
G
Hz.
This a
na
ly
sis i
s p
erform
ed
on
ly
fo
r
the alg
or
it
hm
s that g
a
ve goo
d resu
lt
s
fou
nd
i
n
the
pr
e
vious
sect
i
on
s
.
T
he
t
hr
ee
D
OA
al
gorithm
s
pr
esente
d
he
re
ha
ve
t
he
sam
e
sensibili
t
y
to
the
op
e
rati
ng
fr
e
qu
e
ncy
,
w
hi
ch
is
cl
ea
rly
rem
ark
able
in
Table
6.
B
es
ide
s,
t
he
M
U
SI
C
al
gorithm
can
not
recog
nize
the
seco
nd
a
ng
le
of
arr
i
val
at
0°
.
Howe
ver
,
RO
OT
-
WSF
al
gor
it
h
m
pr
ovide
d
the
best
res
ults
wit
h
alm
os
t no er
ror
.
Table
6
.
T
he
varia
ti
on
of the
nu
m
ber
of sig
na
ls for
dif
fer
e
nt
D
O
A
al
gorith
m
s
Ty
p
e of
DO
A
AOA fo
r
F=2
.4G
H
z
AOA fo
r
5
GHz
-
30°
0°
20°
-
30°
0°
20°
MUSI
C
-
2
4
.4°
u
n
d
etectable
13°
-
21°
u
n
d
etectable
6
.7°
ROOT
-
W
SF
-
30°
0
.00
0
4
°
20°
-
30°
0
.00
09°
20°
ROOT
-
MUS
IC
-
3
3
.62
°
-
0
.00
0
2
°
2
0
.88
°
-
3
0
.78
°
-
0
.00
0
1
3
°
2
0
.04
°
4.
CONCL
US
I
O
N
The
stu
dy
est
ablishe
d
in
this
pap
e
r
is
base
d
on
a
un
if
orm
lin
ear
a
rr
ay
(
UL
A)
of
M
ante
nna
el
em
ents
with
the
inter
-
el
e
m
ent
sp
aci
ng
of
λ/2
,
w
here
al
l
the
so
ur
c
es
are
assum
e
d
unco
rr
el
at
ed
.
W
e
first
eval
uate
d
the
i
m
pact
of
t
he
arr
ay
el
em
e
nts
from
6
to
10
,
in
w
hich
the
ROOT
-
M
USI
C
and
the
RO
OT
-
WSF
al
gor
it
h
m
s
pro
ved
their
e
f
fecti
ven
es
s.
T
hen
we
evalua
te
the
i
m
pact
of
the
num
ber
of
source
s
on
the
DOA
al
gorithm
s.
The
res
ults
cl
early
sh
ow
th
at
the
increas
e
in
the
num
ber
of
s
ource
s
l
eads
to
a
certai
n
com
plexity
in
the
pro
posed
DOA
al
go
rith
m
s,
in
this
case
al
so
,
R
OOT
-
MUS
IC
a
nd
the
RO
OT
-
WSF
al
gorith
m
s
hav
e
achieve
d
the
be
st
resu
lt
s.
Fin
al
ly
,
we
evaluate
the
nu
m
ber
of
s
napsh
ots
or
(
nu
m
ber
of
sam
ples)
that
giv
es
the ide
ntica
l re
su
lt
s.
Fr
om
this
stu
dy,
it
can
be
seen
that
R
O
OT
-
WSF
a
nd
ROOT
-
MU
SIC
al
gorithm
s
hav
e
pro
vide
d
the
best
res
ult
on
the
dif
fer
e
nt
i
m
pacts
that
we
ha
ve
w
orked
with,
the
r
efor
e,
these
t
w
o
te
ch
niques
will
be
the
m
os
t
feasib
le
in
the
upc
om
ing
resea
rch.
As
f
or
the
op
e
rati
ng
fr
e
quenc
y,
the
tw
o
2.4
GH
z
a
nd
5G
H
z
W
i
-
F
i
bands
ga
ve
th
e
best
re
su
lt
with
the
R
O
O
T
-
WSF
al
gorithm
in
com
par
ison
with
t
he
MUSIC
a
nd
ROOT
-
MUSIC
al
go
rithm
.
In
te
rm
s
of
accu
racy,
the
ROOT
-
WSF
al
gorithm
pr
ovides
t
he
m
os
t
accurate
detect
ion
of
the
ang
le
s
of
a
rr
ival
in
the
th
ree
pro
po
se
d
s
cenari
os
with
alm
os
t
no
erro
r.
This
m
akes
it
the
best
cho
ic
e
fo
r
the im
plantat
ion
in
the
sm
art anten
na
syst
em
.
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8708
In
t J
Elec
&
C
om
p
En
g,
V
ol.
9
, N
o.
6
,
Dece
m
ber
2
01
9
:
4873
-
4881
4880
REFERE
NCE
S
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.
Z
.
Chowdhur
y
,
e
t
al
.,
“
A
Com
par
at
iv
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W
ir
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ie
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t
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Huang
,
“
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irnov,
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ase
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f
th
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th
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el
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unic
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rat
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Godara
,
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ti
ons of A
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nna
Arra
y
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Com
m
unic
at
ions.
Pe
r
f
orm
anc
e
Im
prove
m
ent
,
Fe
asibi
l
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,
and
S
y
st
em Con
sidera
t
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ed
,
“
Com
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at
ive
Perform
anc
e
In
vesti
gations
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Stocha
stic
and
Gene
tic
Algorithm
s
Under
Fast
D
y
namic
al
l
y
C
hangi
ng
Enviro
nm
ent
in
Sm
a
rt
Antenna
s
,”
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t
ernati
onal
Jour
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Elec
tric
a
l
and
Compute
r
Engi
ne
ering
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IJ
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)
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pp
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[6]
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ase
m
S
.
S
.
,
et
al
.,
“
Bea
m
form
ing
Algor
it
hm
s
Te
chni
qu
e
b
y
Us
ing
MV
DR
and
LCM
V
,”
Inte
rnation
al
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-
Confe
ren
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Information
Te
c
hnology
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Ap
pli
cations (
IECITA)
,
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S
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S
.
Moghadda
m
,
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al
.,
“
A
nov
el
arr
a
y
g
eometr
y
to
improve
D
OA
esti
m
at
ion
o
f
nar
rowband
so
urc
es
at
the
angles
cl
ose
to
th
e array
end
f
ire.
”
[8]
J
.
Xu,
et
al
.,
“
Joint
Range
and
Angle
Esti
m
at
i
on
Us
ing
MIMO
Rada
r
W
it
h
Freque
nc
y
Dive
rse
Ar
ra
y
,”
IE
E
E
Tr
ansacti
ons on Signal Proce
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.
Q
.
W
ang
,
“
Overvi
ew
of
fre
quency
d
ive
rse
arr
a
y
in
r
ada
r
r
and
nav
iga
t
ion
a
ppli
c
at
ions
,”
I
E
T
Radar,
Sona
r
&
Navi
gati
on
,
201
6.
[10]
S
.
Ouelha
,
et
a
l
.,
“
Im
proving
DO
A
Esti
m
at
ion
Algorit
h
m
s
U
sing
High
-
Resolut
ion
Quadratic
Ti
m
e
-
Frequ
e
n
c
y
Distribut
ions
,”
I
EE
E
Tr
ansacti
o
ns on
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ro
ce
ss
ing
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vo
l. 65,
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5179
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2017.
[11]
J
.
G
.
A
.
Olague
,
e
t
al
.,
“
Eff
icient
Adapt
ive
Algorit
hm
s
for
DO
A
Esti
m
at
ion
in
W
ire
le
ss
Com
m
unic
at
ions
,”
Inte
rnational
Jo
urnal
of
Comm
u
nic
ati
ons
,
Ne
two
rk
and
Syst
em
Sc
ie
nc
es,
v
o
l.
3
,
20
10.
[12]
K
.
A
.
Kum
bar
,
“
Adapti
ve
Beam
form
ing
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ar
t
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for
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ire
le
ss
Com
muni
cation
S
y
ste
m
,”
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rnation
al
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search Journal
of
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n
ee
ring
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og
y (
IRJ
ET)
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02
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[13]
M
.
Deve
ndra
a
nd
K
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Manjunathac
h
ari
,
“
DO
A
esti
m
at
ion
o
f
a
s
y
stem
using
MU
SIC
m
et
hod
,”
Int
ernati
ona
l
Confe
renc
e
on
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ignal
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ss
ing
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ne
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ur
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o,
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n
t
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ntation
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et
hod
for
wideba
nd
DO
A
e
sti
m
at
ion
using
foc
using
oper
ation
,”
IET
Radar,
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r
&
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gati
on
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11
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aghmare
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al
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Bea
m
fo
rm
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art
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DR
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hm
,”
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te
rnat
ional
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o
f
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anc
ed Re
sea
rch
in
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er
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n
ee
ring
&
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ogy
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IJARC
ET)
,
v
ol
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4
,
2
015.
[16]
MA
TL
AB,
“
The Mat
hW
orks,
Di
rec
t
ion
of
Arriva
l
Esti
m
a
ti
on,
”
In
c,
N
at
i
ck, Unit
e
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B
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Boustani
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et
al
.,
“
Perform
anc
e
anal
y
s
is
of
Dire
ct
ion
Of
Arriva
l
esti
m
ati
on
under
har
d
condi
ti
on
,”
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h
Inte
rnational
Co
nfe
renc
e
on
Opti
mization
and
A
p
pli
cations (
ICOA)
,
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m
edi
a,
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-
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,
2
018.
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S
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Lukose
,
“
A St
ud
y
on
Vari
ous
T
y
p
es
of
B
ea
m
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orm
ing
Algorit
h
m
s
,”
IJS
TE
,
vol
.
2,
2
010
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[19]
J
.
Capon
,
“
High
-
resolut
ion
fre
qu
e
nc
y
-
w
ave number
spec
tral
ana
l
ysis
,”
Proc
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I
EEE
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[20]
N
.
Nem
ri,
e
t
al
.,
“
Sy
n
the
sis
and
Im
ple
m
ent
at
ion
(In
STM8S
)
of
Phased
Circ
ul
ar
Anten
na
Arra
y
s
Us
ing
Ta
guchi
Method
,”
Int
ernati
onal Journal of
E
le
c
tric
al
and
Computer
Eng
i
nee
ring (
IJE
C
E)
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2016
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[21]
MA
TL
AB,
“
The
MathWorks
,
Dire
ction
of
Arriva
l
Esti
m
ation
wi
th
Bea
m
sca
n,
M
VD
R
,
and
MU
S
IC,
”
Inc
,
Natick,
Unite
d
St
at
es
.
[22]
E
.
T
.
Aung
and
S
.
S
.
Y
.
Mon
,
“
Perform
anc
e
compari
son
of
DO
A
esti
m
at
i
on
al
gorit
hm
s
for
sm
art
ant
enna
,”
IJE
CSE
,
vo
l.
3,
pp.
167
-
174
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[23]
T
.
B
.
La
v
at
e
,
e
t
al
.,
“
Perform
an
ce
Anal
y
sis
of
MU
SIC
and
ES
PR
IT
DO
A
Esti
m
at
ion
Algorit
h
m
s
for
Adapti
ve
Arra
y
the Sm
art
Antenna
in
Mob
il
e
Com
m
unic
at
i
on
,”
In
te
rnat
ion
al
Journal
of
Co
mputer
Net
wo
ks
(
IJCN
)
,
vol. 2.
[24]
Viber
g
M
.
,
et
al
.,
“
Dete
c
ti
on
and
esti
m
at
ion
in
s
e
nsor
arr
a
y
s
usin
g
weight
ed
subs
pac
e
f
it
t
ing,
”
IE
EE
Tr
ans.
Signal
Proce
ss
,
vol
.
39
,
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2436
-
2449
,
1991
.
[25]
Y
.
Huang
and
L
.
F
.
Fam
il
,
“
Buil
ding
Heigh
t
Esti
m
at
ion
Us
in
g
Multi
base
Li
n
el
-
Band
Sard
at
a
and
Polari
m
et
r
i
c
W
ei
ghte
d
Subs
p
ac
e
Fitt
ing
Me
th
ods
,”
Univ
ersity
of
R
enne
s 1
,
Inst
i
tut
e
of
Telecom
municat
ion
and
El
e
ct
ronics
.
[26]
“
Dire
ct
ion
o
f
a
rr
iva
l
esti
m
ation
m
et
hods
,”
CRC
Press LL
C
,
2004
.
[27]
B.
A.
Johns
on,
e
t
al
.,
“
The
Role
of
Subs
pac
e
Swa
p
in
Maximum
Li
kelihood
Est
i
m
at
ion
Perform
anc
e
Brea
kdown
,”
IEE
E
Proc
.
of
In
t.
Con
f. on Ac
ou
stic
s,
Sp
eech, an
d
Signal P
roc
essing,
pp
.
2469
-
24
72,
2008
.
[28]
“
Arra
y
and
Sta
tis
ti
ca
l
Signa
l
Pro
ce
ss
ing
,”
A
cadem
ic
Press Librar
y
in
Signal P
roc
essing.
A
cade
mi
c
Press
,
2013
.
[29]
M
.
U
.
Shahid,
e
t
al
.,
“
Com
par
at
i
ve
ana
l
y
sis
be
twee
n
dir
ec
t
ion
of
arr
ival
al
gor
it
hm
s
,”
Inte
rnat
io
nal
Confe
renc
e
o
n
Infoc
om Tec
hno
l
ogie
s and
Unm
a
nned
Syst
ems (
T
rends and
Fut
ur
e
Direc
ti
ons)
(
I
CT
US
)
,
Dubai, p
p.
451
-
454
,
201
7
.
[30]
N
.
A
.
Bai
g
and
M
.
B
.
Mali
k
,
“
Com
par
ison
of
Dire
ct
ion
of
Arriva
l
(DO
A)
Esti
m
at
ion
Techn
ique
s
for
Closely
Space
d
Ta
rg
et
s
,”
Int
ernati
onal
J
ournal
of Fut
ure
Computer
and
Comm
unic
ati
on,
v
ol. 2,
2013
.
[31]
Y
.
Khm
ou,
et
a
l
.,
“
Com
par
at
ive
Stud
y
bet
we
en
Sever
a
l
Dire
ct
i
ons
of
Arriva
l
Esti
m
at
ion
Me
t
hods
,”
Journal
of
Tele
communic
a
t
ions
and
Infor
mation
Techno
l
ogy,
Na
ti
onal
I
nstit
ute
of
Telecomm
unic
at
ions,
W
arsa
w,
vol
.
1,
pp.
41
-
48
,
2014
.
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
Elec
&
C
om
p
En
g
IS
S
N: 20
88
-
8708
Perf
orma
nce
analysis
of
direc
ti
on
of arri
val
algorit
hms fo
r
smart a
nten
na
(
Bti
ssa
m
B
oustan
i)
4881
BIOGR
AP
H
I
ES
OF
A
UTH
ORS
Btissam
BOUS
TAN
I
born
in
M
ohamm
edi
a,
Mo
roc
co
on
June
2
4,
1989
.
In
2012
She
had
got
h
e
r
li
c
ense
degr
ee
i
n
ph
y
si
cal
sci
en
ce
for
the
eng
in
ee
r
,
a
t
th
e
Univ
ersity
Hass
an
II
Moham
m
edi
a
Casabl
a
n
ca
-
Mo
roc
co
(FS
TM)
,
the
n
she
had
g
ot
a
Master
'
s
d
egr
ee
in
s
y
st
em
and
computer
signal
s
at
Fez
Univer
sit
y
of
Science
s
Dhar
El
Mahra
z
.
She
is
cur
ren
tly
a
Ph.D.
student
in
th
e
La
bora
tor
y
of
El
e
ct
roni
cs,
En
erg
y
,
Autom
at
i
cs
and
Data
Pr
oce
ss
ing
(EE
A
&T
I)
Hass
an
I
I
Univer
sit
y
,
Moh
amm
edi
a
-
Casablanc
a
,
Morocc
o
.
Her
works
studie
s
a
nd
int
er
ests
are
foc
used
on
the
opti
m
izat
ion
of
the
per
form
a
nce
of
sm
art
antenna
s
y
st
em
to
c
rea
t
e
a
be
amform
ing
adj
ustable
to
the
nee
ds
of
the
s
y
stem
improvem
ent
s
,
assuring
to
loc
at
e
and
t
rac
k
the
desir
ed
signal
,
under
the
supervision
of
Pr.
A.
Baghd
ad,
Profess
or
in
El
e
ct
r
ic
a
l
eng
in
ee
ring
d
epa
r
tment
at
the
sam
e
Univer
sit
y
.
Ab
den
naceur
BAGHDAD
is
a
holde
r
of
a
do
ctorat
e
in
the
Elec
troni
cs
in
1992
a
t
the
Univ
ersi
t
y
of
Li
lle
–
Franc
e.
He
is
Univ
er
sit
y
Profess
or
(
PES
)
at
the
Uni
ver
sit
y
Hass
an
I
I
Moham
m
edi
a
Casabl
an
ca
-
Morocc
o
(FS
TM)
where
he
t
ea
ch
e
s
the
el
e
ct
ron
ic
s
,
H
y
per
fr
eque
nc
ie
s,
ant
enn
a
and
te
l
ec
om
m
unic
at
i
on.
He
is
a
m
ember
of
the
l
ab
ora
tor
y
EE
A&T
I
(Elec
ton
ic
s,
E
ner
g
y
,
Autom
ati
c
and
info
rm
at
ion
Proce
ss
ing).
The
rese
ar
ch
works
of
A.
Baghd
ad
conc
ern
s
th
e
comm
unic
at
ion
and
Inform
at
ion
Technol
og
y
(
El
e
ct
roni
cs
S
y
st
ems
and
Tele
c
om
m
unic
at
ion).
He
supervise
s
doct
ora
l
th
ese
s
a
nd
he
is
a
co
-
author
of
sev
era
l
n
at
ion
al
and
int
er
nat
ion
al
pub
li
c
ations.
He
was
a
m
ember
of
stee
r
i
ng
comm
it
te
es
o
f
three inte
rn
at
i
o
nal
congr
esses i
n
the sam
e
dom
a
in
of
r
ese
ar
ch.
Aïcha
SA
HEL
is
a
hold
er
of
a
doct
or
at
e
in
Elec
tron
ic
s
and
I
m
age
Proce
ss
in
g
in
1996
at
the
Univer
sit
y
of
Poiti
ers
-
Fran
ce
.
She
is
uni
ver
sit
y
P
rofe
ss
o
r
at
the
Unive
rsit
y
Hass
an
II
Moham
m
edi
a
–
Casabl
an
ca
-
M
oroc
co
(FS
TM)
where
she
t
ea
ch
es
el
e
ct
roni
cs,
si
gnal
proc
essing
,
image
proc
essi
ng
and
Te
leco
m
m
unic
at
ion.
She
is
a
m
emb
er
of
the
la
bor
at
or
y
EE
A&
TI
(El
e
ct
roni
cs,
E
lectr
ot
ec
hni
cs,
Au
tomati
c
and
In
fo
rm
at
ion
proc
essing).
The
rese
arch
works
of
A.
SA
HEL
conc
er
n
the
Com
m
u
nic
a
ti
on
and
I
nform
at
ion
Te
c
hnolog
y
(E
lectr
onic
s
S
y
stems
,
Signal
/Image
Pr
oce
ss
ing
and
Tel
ec
om
m
unic
at
ion
).
She
co
-
superv
ises
doct
ora
l
th
e
ses
and
she
is
a
co
-
aut
hor
of
sev
era
l
nationa
l
an
d
interna
t
iona
l
pu
bli
c
at
ions.
She
is
a
m
ember
of
fin
anc
ed
rese
arch
proje
c
ts.
She
wa
s
a
m
ember
of
st
ee
ring
comm
it
tees
of
thre
e
in
te
r
nat
ion
al
congr
esses
in
the
sam
e
dom
ai
n
of
r
ese
ar
ch.
Ab
delmaji
d
BA
DR
I
is
a
holde
r
of
a
doct
or
ate
i
n
El
e
ct
roni
cs
an
d
Im
ag
e
Proce
ss
ing
in
1992
a
t
the
Univer
si
t
y
o
f
Poiti
ers
-
Fra
nce
.
In
1996,
h
e
obtained
the
dipl
om
a
of
th
e
aut
hori
za
t
ion
to
Mana
ge
R
ese
ar
c
hes
(HD
R)
to
th
e
Univer
sit
y
of
Poiti
ers
-
Fran
ce
,
on
th
e
imag
e
p
roc
essing.
He
was
a
Univer
si
t
y
Profess
or
(PES
-
C)
at
the
Univ
ersity
Hass
an
II
Moham
m
edi
a
-
C
asa
bla
n
ca
Morocc
o
(FS
T
M).
In
2018
,
h
e
be
ca
m
e
s
dir
e
ct
or
of
the
superior
schoo
l
of
technolog
y
of
Casabl
an
ca
Morocc
o
(EST)
.
He
is
a
m
ember
o
f
the
la
bora
tor
y
EE
A&TI
(Elec
toni
cs,
En
er
g
y
,
Autom
at
ic
and
i
nform
at
ion
Proc
essing)
which
h
e
m
ana
ged
sin
ce
1996.
Th
e
rese
ar
ch
works
of
A.
Badri
con
ce
rns
the
comm
unic
ation
and
Inf
orm
at
ion
Tech
nolog
y
(
Elec
tro
nic
s
S
y
stems
,
Signal
/Image
Proce
ss
ing
and
T
el
e
comm
unic
at
i
on).
He
is
qua
l
ifi
ed
b
y
CNU
-
Franc
e
in
61
st
sec
ti
on:
informa
ti
cs
engi
ne
eri
ng
,
aut
om
at
ic
and
s
igna
l
proc
essing
.
He
m
ana
ged
seve
ra
l
do
ct
ora
l
the
ses.
He
is
a
c
o
-
aut
hor
of
seve
ral
national
and
int
ern
at
ion
al
pu
bli
c
at
ions.
He
is
responsible
for
seve
ral
r
ese
ar
ch
proje
ct
s
fin
anced
b
y
th
e
m
ini
str
y
or
b
y
th
e
in
dustria
li
sts
.
He
was
m
ember
of
seve
ral
comm
it
t
ee
s
of
progra
m
s
of
int
ern
at
ion
al
conf
ere
nc
es
and
pre
sident
of
thre
e
interna
t
ional
congr
esses
in
th
e
sam
e
dom
ai
n.
He
is
a
m
ember
and
responsibl
e
in
seve
r
al
sc
ie
nt
i
fic
associa
t
ions
in
tou
ch
with
his
dom
ai
n
of
rese
a
rch
.
Evaluation Warning : The document was created with Spire.PDF for Python.